On two-grid convergence estimates

Robert D. Falgout, Panayot S. Vassilevski, Ludmil T. Zikatanov

Research output: Contribution to journalArticlepeer-review

72 Scopus citations


We derive a new representation for the exact convergence factor of classical two-level and two-grid preconditioners. Based on this result, we establish necessary and sufficient conditions for constructing the components of efficient algebraic multigrid (AMG) methods. The relation of the sharp estimate to the classical two-level hierarchical basis methods is discussed as well. Lastly, as an application, we give an optimal two-grid convergence proof of a purely algebraic 'window'-AMG method. Published in 2005 by John Wiley & Sons, Ltd.

Original languageEnglish (US)
Pages (from-to)471-494
Number of pages24
JournalNumerical Linear Algebra with Applications
Issue number5-6
StatePublished - Jun 2005

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Applied Mathematics


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